" (ii) "(cot theta)/((csc theta+1))+((csc theta+1))/(cot theta)=2sec theta

(cot theta)/((cosec theta+1))+((cosec theta+1))/(cot theta)=2sec theta

Prove each of the following identities : (i) (tan theta)/((sec theta -1)) + (tan theta)/((sec theta +1)) = 2 "cosec" theta (ii) (cot theta)/(("cosec" theta +1))+ (("cosec" theta +1))/(cot theta ) = 2 sec theta

1+(cot^(2)theta)/(1+csc theta)=csc theta

Prove that (sin theta)/((cot theta+cosec theta))-(sin theta)/((cot theta-cosec theta))=2

(cot theta+csc theta-1)/(cot theta-csc theta+1)=(1+cos theta)/(sin theta)

(sin theta)/(cot theta+cosec theta)=2+(sin theta)/(cot theta-cosec theta)

csc theta(1+cos theta)(csc theta-cot theta)=1

Prove that (cot theta+csc theta-1)/(cot theta-csc theta)=(cot theta+csc theta)(cot theta+csc theta-1)

(tan theta)/(sec theta+1)+(cot theta)/(csc theta+1)=csc theta+sec theta-csc theta sec theta

(1+cosec theta - cot theta)/(1+cosec theta + cot theta)=